There are a couple common reason that dlvr.it cannot successfully post updates to your Facebook page:
Facebook imposed rate limits
Facebook's imposes rate limits on the number of items that can be posted to Facbeook by each user. dlvr.it can only post what they allow us to post, and when you post too many items, they disable posting for your account for a period of time. Once Facebook rate limit period ends, dlvr.it will begin posting new items to your Facebook page again.
Unfortunately, Facebook does not make their rate limits public, so we have little guidance on how Facebook applies their rate limit rules.
dlvr.it has lost authorization to post to your Facebook page.
Here are details on why dlvr.it can lose authorization to post to Facebook and how you can reauthorize dlvr.it to post on your behalf: